What kind of transformation converts the graph of f(x) = -8(x + 5)^2 - 10 into the graph of g(x) = -8(x + 4)^2 - 10? Choices: (A)translation 1 unit up (B)translation 1 unit left (C)translation 1 unit right (D)translation 1 unit down

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = -8(x + 5)^2 - 10 is in vertex form, where the vertex is at the point (-5, -10).Compare Vertices: Identify the vertex of the function g(x). The function g(x) = -8(x + 4)^2 - 10 is also in vertex form, where the vertex is at the point (-4, -10).Determine Shift Direction: Compare the vertices of f(x) and g(x) to determine the type of transformation. The vertex of f(x) is (-5, -10) and the vertex of g(x) is (-4, -10). The y-coordinates are the same, so there is no vertical shift. The x-coordinate of g(x) is 1 unit greater than the x-coordinate of f(x), indicating a horizontal shift.Match Transformation: Determine the direction of the horizontal shift. Since the x-coordinate of the vertex of g(x) is 1 unit greater than the x-coordinate of the vertex of f(x), the graph has shifted 1 unit to the right.Match the transformation to the given choices. The graph of f(x) has been shifted 1 unit to the right to obtain the graph of g(x). This corresponds to choice (C) translation 1 unit right.

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What kind of transformation converts the graph of $f(x) = -8(x + 5)^2 - 10$ into the graph of $g(x) = -8(x + 4)^2 - 10$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit up $\newline$ (B) translation $1$ unit left $\newline$ (C) translation $1$ unit right $\newline$ (D) translation $1$ unit down

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -8(x + 5)^2 - 10

into the graph of

g(x) = -8(x + 4)^2 - 10

\newline

Choices:

\newline

(A) translation

1

unit up

\newline

(B) translation

1

unit left

\newline

1

unit right

\newline

(D) translation

1

unit down

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = -8(x + 5)^2 - 10$ is in vertex form, where the vertex is at the point $(-5, -10)$ .
Compare Vertices: Identify the vertex of the function $g(x)$ . The function $g(x) = -8(x + 4)^2 - 10$ is also in vertex form, where the vertex is at the point $(-4, -10)$ .
Determine Shift Direction: Compare the vertices of $f(x)$ and $g(x)$ to determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(-5, -10)$ and the vertex of $g(x)$ is $(-4, -10)$ . The $y$ -coordinates are the same, so there is no vertical shift. The $x$ -coordinate of $g(x)$ is $1$ unit greater than the $x$ -coordinate of $f(x)$ , indicating a horizontal shift.
Match Transformation: Determine the direction of the horizontal shift. Since the $x$ -coordinate of the vertex of $g(x)$ is $1$ unit greater than the $x$ -coordinate of the vertex of $f(x)$ , the graph has shifted $1$ unit to the right.
Match Transformation: Determine the direction of the horizontal shift. Since the $x$ -coordinate of the vertex of $g(x)$ is $1$ unit greater than the $x$ -coordinate of the vertex of $f(x)$ , the graph has shifted $1$ unit to the right.Match the transformation to the given choices. The graph of $f(x)$ has been shifted $1$ unit to the right to obtain the graph of $g(x)$ . This corresponds to choice (C) translation $1$ unit right.